In Ref. [1]}, the authors showed that cold DBI inflation
model can be reconciled with the observations, removing the
aforementioned inconsistencies, provided that the strong dissipation
regime of Dirac-Born-Infeld warm inflation (DBIWI) is achieved. This
is also because the WI scenario violates the Lyth bound. However, the
work done in Ref. [1]} made use of a phenomenological
dissipation coefficient, assuming it to be independent of the
temperatureThe stringent lower bound on tensor-to-scalar
ratio can be relaxed in other DBI setups without dissipation, for
instance, in multi-brane [3]} and
multi-field [4]} models. However, almost all
explicit particle physics realizations of WI result in an explicit
temperature dependent dissipation
coefficient [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Besides
this, pushing WI into the strong dissipation regime is challenging
due, again, to the aforementioned problem related to the appearance of
a growing/decreasing function in the power spectrum, which tend to
lead to results inconsistent with the observations, e.g., for the
spectral tilt [11]}. Although there have been some
previous papers considering DBIWI
realizations [1]}, [13]}, [14]}, none of
them made an investigation of the role of the sound speed on the
backreaction of the radiation perturbations on the inflaton
ones. Thus, none of the earlier references on DBIWI have studied how
the growing/decreasing function in WI gets affected by the sound
speed, which requires a detailed study of the perturbations in DBIWI.
Taken all together, the purpose of this paper is to cover this issue
and to proper understand the primordial perturbations in DBIWI and the
consequences that it brings to model realizations, as far as the
observations constraints are taken into account. Our results show that
DBIWI is able to go into the strong dissipation regime for
well-motivated field theory realizations of WI that result in explicit
temperature dependent dissipation coefficients. Our results also shed
new light on the potential use of DBI type of models in the context of
WI.
